Multiplication principle - practice problems
Number of problems found: 435
- Conditional probability
Suppose a batch contains 10 items of which 4 are defective. Two items are drawn at random from the batch one after the other, without replacement. What is the probability that: I) both are defective? Ii) the second item is defective?
- A committee
A committee of 6 is chosen from 8 men and 7 women. Find how many committees are possible if a particular man must be included.
- Equilateral 75284
Given are 6 line segments with lengths of 3 cm, 4 cm, 5 cm, 7 cm, 8 cm, and 9 cm. How many equilateral triangles can make from them? List all the options.
- Overbooking flight
A small regional carrier accepted 12 reservations for a particular flight with 11 seats. 7 reservations went to regular customers who will arrive for the flight. Each of the remaining passengers will arrive for the flight with a 49% chance, independently
- A bag 4
A bag contains 18 balls that differ only in colour, 11 are blue and 7 red. If two balls are picked, one after the other without replacement, find the probability that both are (i) Blue (ii) Of the same colour (iii) Of different colours
- Four digit codes
Given the digits 0-7. If repetition is not allowed, how many 4 digit codes that are greater than 2000 and divisible by 4, are possible?
- In an
In an square ABCD n interior points are chosen on each of its side. Find the number of all triangles whose vertices X, Y, Z lie at the this points and on different sides of the square.
- Indistinguishable 74294
We have eight compartments where we put three indistinguishable balls and two distinguishable ones. How many options do we have?
- Probability 73714
I roll six six-sided dice; what is the probability that exactly three threes will fall?
- Menu choice
In a Jollibee, you have a menu choice of C1, C2, and C3. For a dessert, you have a choice of ice-cream and mango peach. How many different options do you have?
- A bag 2
A bag contains 7 green and 8 red jellybeans. How many ways can 5 jellybeans be withdrawn from the bag so that the number of green ones withdrawn will be less than 4?
- Calculation 73364
From the number 5,4,0,7,8, create three-digit numbers so that they do not repeat and solve the problem by calculation.
- Four-digit 73114
How many four-digit numbers can we assemble from the digits 2, 6, 3, 5, 1, and 9 if the numerals in the number cannot be repeated?
- T-shirts 73074
Dušan has 8 T-shirts and three pairs of shorts in his closet. How many ways can he dress for school?
- Probability 73054
We roll six dice. What is the probability that: a) a six falls twice b) six falls four times
- Between 72924
How many ways do we know to select three cards from a deck of seven cards so that there are two red and one green between them?
- Probability 72324
We used the digits 2, 3, 4, 5, and 7 when entering the PIN code, and we only used each digit once. What is the probability that someone will guess our PIN code on the first try?
- Groups 72194
I have eight groups. How could they place first, second and third?
- Three-digit 72184
How many three-digit numbers can be created from the numbers 1, 2, 3, and 4 if you can repeat them?
- Probability 71784
What is the probability that if you roll the die twice, the sum of 12 will fall?